How can I select and delete a drawn graphic after it has been saved in the document?

When I have a problem like yours, I create a large rectangle selection starting outside of the text frame.

Just click outside the text frame, keep the mouse button pressed and draw a rectangle which also comprises your oval but not the whole text frame. This should select your oval. (If there are other objects behind the text frame, these would be selected as well.)

Then press Delete.

In addition to Arnis' useful advice, there's also some chance that you might have to Ungroup some elements if what you select turns out to be more than just the oval.

Just ctrl-click on whatever is in front and send that to the back. You should then be able to select your oval and delete it. If you still can't select it, then keep sending objects in front to back until you get to it.

Visualize a stack of plates. Keep moving the top one to the bottom until you get to the plate that you want.